Scala analysis: xen09-wilson-marwa-17b-09
Marwa permutation 9 from Figure 17b, Archytas 36/35 28/27 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 4/3 498.044999 perfect fourth 4: 5/3 884.358713 major sixth, BP sixth 5: 12/7 933.129094 septimal major sixth 6: 16/9 996.089998 Pythagorean minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 8/7 231.1741 septimal whole tone 2: 9/8 203.9100 major whole tone 3: 28/27 62.9609 Archytas' 1/3-tone 4: 5/4 386.3137 major third 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 28/27 62.9609 Archytas' 1/3-tone 7: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 2 7/6 266.871 cents septimal minor third 2: 3 9/7 435.084 cents septimal major third, BP third 2: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 3: 1 6/5 315.641 cents minor third 3: 4 4/3 498.045 cents perfect fourth 3: 1 81/56 638.994 cents 3: 1 35/24 653.185 cents septimal semi-diminished fifth 4: 1 48/35 546.815 cents septimal semi-augmented fourth 4: 1 112/81 561.006 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 5/3 884.359 cents major sixth, BP sixth 5: 1 54/35 750.725 cents septimal semi-augmented fifth 5: 3 14/9 764.916 cents septimal minor sixth 5: 2 12/7 933.129 cents septimal major sixth 5: 1 15/8 1088.269 cents classic major seventh 6: 1 8/5 813.686 cents minor sixth 6: 1 7/4 968.826 cents harmonic seventh 6: 2 16/9 996.090 cents Pythagorean minor seventh 6: 2 27/14 1137.039 cents septimal major seventh 6: 1 35/18 1151.230 cents septimal semi-diminished octave Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 231.2 435.1 498.0 884.4 933.1 996.1 1200.0 231.2 : 203.9 266.9 653.2 702.0 764.9 968.8 1200.0 435.1 : 63.0 449.3 498.0 561.0 764.9 996.1 1200.0 498.0 : 386.3 435.1 498.0 702.0 933.1 1137.0 1200.0 884.4 : 48.8 111.7 315.6 546.8 750.7 813.7 1200.0 933.1 : 63.0 266.9 498.0 702.0 764.9 1151.2 1200.0 996.1 : 203.9 435.1 639.0 702.0 1088.3 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 386.3137 cents 175/144, 337.5433 cents 36/35, 48.7704 cents 2: 111.7313 .. 449.2746 cents 175/144, 337.5433 cents 64/75,-274.5824 cents 3: 315.6413 .. 653.1846 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 4: 546.8154 .. 884.3587 cents 175/144, 337.5433 cents 1152/1225,-106.3692 cents 5: 750.7254 .. 1088.2687 cents 175/144, 337.5433 cents 162/175,-133.6333 cents 6: 813.6863 .. 1151.2296 cents 175/144, 337.5433 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 3.515014 Largest / Average step : 2.253497 Largest / Smallest step : 7.921072 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 179.82213 cents, oct.: 1258.75488 cents Scale is not proper Step pattern alph. order: ABCDECB Step pattern size order : DCBEABC Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.577632 Lumma stability : 0.081284 Lumma impropriety factor : 0.651213 Rothenberg efficiency : 0.423129 redundancy: 0.576871 Efficiency x scale size : 2.961905 Number of different interval sizes : 26 = 4.33333 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 245/243, 14.1905 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 6 Formal octave complements present : 1 = 14.2857% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 7 Odd number limit : 81 (O: 81 U: 81) Highest odd numerator or denominator: 9 Scale harmonicity : 0.031896 Average absolute harmonicity : 0.233985 Specific harmonicity : 0.178561 Fundamental : 1/63, -5.9773 octaves, 4.1528 Hz. Guide tone : 720, 9.4919 octaves, 188370.407 Hz. Exponens Consonantiae : 4.536000E+04, 15.46913 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 46.5, average 6.64286 Mersenne's string divisions : 159600 Sum of van Prooijen's expressibility: 4.77477, average 0.68211 Sum of Tenney's harmonic distance : 10.18647, average 1.45521 Vogel's harmonic complexity : 12.00000 Wille's k value : 52 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 75.69878, average 2.70353 Lattice compactness (without 2's) : 49.37538, average 1.76341 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 4 1.71429 12 1 3: -2 .. 2 -0.14286 7 2 5: 0 .. 1 0.14286 1 1 7: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-3 / 7 =-0.42857 Average absolute exponent except 2's: 11 / 7 = 1.57143 Scale is weakly epimorphic with val: <7 10 15 18| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 12 17 18|
FIT/MODE
7: 1 1 1 2 0 1 1 N T3 SD: 53.3302 c. M: 92.2270 c. 8: 2 1 0 3 0 1 1 N SD: 40.5609 c. M:-68.8259 c. 9: 2 1 1 3 0 0 2 N SD: 37.9338 c. M: 62.7567 c. 10: 2 2 0 3 1 0 2 N SD: 30.2683 c. M:-44.9159 c. 11: 2 2 1 3 1 0 2 N G SD: 27.0653 c. M:-48.6891 c. 12: 2 2 1 4 0 1 2 N SD: 22.5642 c. M: 35.0841 c. 14: 3 2 1 4 1 1 2 N SD: 20.2517 c. M:-32.4814 c. 16: 3 3 1 5 0 1 3 N SD: 19.9075 c. M: 33.1291 c. 17: 3 3 1 5 1 1 3 N T3 SD: 17.8018 c. M: 37.2999 c. 19: 4 3 1 6 1 1 3 N SD: 11.7899 c. M:-21.4575 c. 22: 4 4 1 7 1 1 4 N T3 SD: 9.2167 c. M: 14.2718 c. 31: 6 5 2 10 1 2 5 N SD: 6.2542 c. M:-10.3616 c. 36: 7 6 2 12 1 2 6 N SD: 6.2282 c. M:-15.6413 c. 41: 8 7 2 13 2 2 7 N SD: 3.3229 c. M: 6.3099 c. 53: 10 9 3 17 2 3 9 N SD: 3.2012 c. M: 4.8954 c. 58: 11 10 3 19 2 3 10 N SD: 2.8492 c. M:-5.2965 c. 72: 14 12 4 23 3 4 12 N SD: 1.9975 c. M:-3.9100 c. 77: 15 13 4 25 3 4 13 N SD: 2.0662 c. M:-3.9530 c. 94: 18 16 5 30 4 5 16 N SD: 1.5554 c. M: 3.5076 c. 99: 19 17 5 32 4 5 17 N SD: 1.0993 c. M: 2.1506 c. 130: 25 22 7 42 5 7 22 N SD: 0.9607 c. M:-1.7951 c. 171: 33 29 9 55 7 9 29 N SD: 0.2475 c. M:-0.4049 c. 441: 85 75 23 142 18 23 75 N SD: 0.1589 c. M:-0.2901 c. 571: 110 97 30 184 23 30 97 N SD: 0.1568 c. M:-0.4049 c. 612: 118 104 32 197 25 32 104 N SD: 0.1349 c. M:-0.2100 c. 665: 128 113 35 214 27 35 113 N SD: 0.1405 c. M: 0.1969 c. 742: 143 126 39 239 30 39 126 N SD: 0.1261 c. M:-0.2774 c. 836: 161 142 44 269 34 44 142 N SD: 0.1023 c. M: 0.1559 c. 935: 180 159 49 301 38 49 159 N SD: 0.0984 c. M: 0.1581 c. 1007: 194 171 53 324 41 53 171 N SD: 0.0968 c. M: 0.1482 c. 1106: 213 188 58 356 45 58 188 N SD: 0.0542 c. M: 0.0911 c. 1277: 246 217 67 411 52 67 217 N SD: 0.0375 c. M: 0.0987 c. 1677: 323 285 88 540 68 88 285 N SD: 0.0391 c. M:-0.0778 c. 1718: 331 292 90 553 70 90 292 N SD: 0.0490 c. M: 0.0747 c. 1848: 356 314 97 595 75 97 314 N SD: 0.0240 c. M:-0.0569 c. 2019: 389 343 106 650 82 106 343 N SD: 0.0280 c. M:-0.0467 c. 2289: 441 389 120 737 93 120 389 N SD: 0.0279 c. M:-0.0450 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 91.2019 cents 3 x x 4:5 x x 6 S SD: 0.0000 cents 4 x 5 x x x 7:8 SD: 18.6246 cents 5:6 x 7:8 x 9:10 S SD: 28.0902 cents 6:7 x 8:10 x 11:12 S SD: 12.8254 cents 7:8:9 x x 12 x 14 S SD: 0.0000 cents 8:9:10:11:13 x 14:16 SD: 15.4779 cents 9:10 x 12:15 x 16:18 S SD: 9.7541 cents 10:11:13 x x 17:18:20 SD: 14.7198 cents 11:13:14:15:18:19:20:22 SD: 12.6847 cents 12:14:15:16:20 x 21:24 S SD: 11.0506 cents 13:15:17 x x 22:23:26 SD: 8.2563 cents 14:16:18:19:23:24:25:28 SD: 5.7480 cents 16:18 x 21:27 x 28:32 SD: 10.3779 cents 17:19:22:23:28:29:30:34 SD: 7.7098 cents 18:21:23:24:30:31:32:36 SD: 5.4457 cents 21:24:27:28:35:36:37:42 SD: 2.2181 cents 36:41:46:48:60:62:64:72 SD: 2.0953 cents 42:48:54:56:70:72:75:84 SD: 1.1016 cents 63:72:81:84:105:108:112:126 S SD: 0.0000 cents